Face,
Sympathy, here, at some stages in the past Ds was distinctly unpleasant at home. As was I in my teens too. Caused mainly by unhappiness and insecurity in both our cases.
For Ds it did improve when I recognised that DH was manipulative, as DS had been telling me. And I chose which battles to pick. And I told him how good he looked, praised him for normal stuff, and told him often how much I loved him.
It sounds as though, whether consciously or not your DH is depressed and is again consciously or not being manipulative. And just his depression , your concern for him and your other child will be making her feel, whether or not you intend this ( and I'm sure you dont) the left out one and insecure. It then starts a vicious circle where she doesn't work at school, etc and you are piggy in the middle.
Whether or not she or others are on the AS spectrum, , there is some excellent advice, Google it, on how to cope with AS style arguments. In brief, don't. They just persist. DH who is AS does, DS who is v slightly does, and like your DD continues to follow me arguing. V wearing. Especially when combined with near physical threatening.
I think people have offered excellent suggestions but I'm going to make another couple. .
One, cherish yourself. Regular small bits of pleasure for you, eg a nice bath, half an hour to read a book, laughing with a friend, going to see an exhibition, will help you. You will be more energised, find balance, relax, and that will help everyone.
Two, The next stage is to take your DD with you. Go and get a pedicure together. Tell her what nice feet she has. If she wants vile nail polish, let her have it! Consult her on yours and go along with her suggestion.
If she doesn't want to come, say "Shame, it would have been good to go with you, " and leave it at that. . when you go back say what a nice time you had but it would have been more fun if she had been there. Then think about whether there is something that you've never done, prob quite minor, that she could be part of. Eg , " I've always wanted to go skating but my friends would laugh at me, will you come? " Or "I've always wanted to learn how to make pasta, will you come? " Or, "I need new jeans, will you come and tell me what looks good on me?" And point out afterwards how much you appreciated her coming. Find stuff to laugh about with her. Be the one who needs her advice. Catch her being good, as they used to say.
We still have rows on these occasions but DS said recently, " even though we had some disagreements, we still had a good time, didn't we?" Which I regard as triumph.
But most of all, make time for you. . PM me if you want.